Extra material in answers turned out to be words or phrases associated
with numbers. Intersecting answers had different material leading to
the same number. The corresponding clue answers were one letter too
short for their allotted positions, leaving some cells unfilled. When
the numbers associated with the extra material were written in the
empty cells, a 3 by 3 magic square was formed, with rows of 25, 8, 12;
2, 15, 28; and 18, 22, 5.

The message spelled out by the extra letters in wordplay was LETTER
COUNT GIVES A SECOND MAGIC SQUARE. Counting the number of letters in
each element of the first magic square gave the following: TWENTY FIVE
(10), EIGHT (5), TWELVE (6); TWO (3), FIFTEEN (7), TWENTY EIGHT (11);
EIGHTEEN (8), TWENTY TWO (9), FIVE (4). Remarkably, the letter counts
also formed a 3 by 3 magic square, with the sum of each row, column and
diagonal equal to 21. When TWENTY ONE was written in the cells which
were originally empty, in grid order, new words were formed, and this
was the grid to be submitted. Gregson noted that TWENTY TWO, THIRTY ONE
and THIRTY TWO would also lead to real words, but these were red
herrings carefully planted by Leo.

The significance of the title could be explained in two ways. The
square root of 576 is 24, and there are 24 letters in FIVE HUNDRED AND
SEVENTY SIX. Furthermore, 24 was the difference between the row totals
of the two magic squares, ie 45 – 21.

Gregson was left wondering if any other magic squares exhibit this type
of duality.

Extra material in clues, and extra letters in wordplay, are indicated
by [].